
where in the first and last line we have used the fact that \(\iota =m\circ q\) , in the second line [1]} which proves that the natural morphism \(q^!m^\ast (j_0)_!(j_0)^!\rightarrow q^\ast m^\ast (j_0)_!(j_0)^!\)  is an isomorphism and in the third and fifth line the isomorphisms built in [1]} using the six-functor formalism in the Cartesian square of closed subspace of \(X\) , Using the fact that \(U^{an}=\tilde{U}^{an}_0\cup \tilde{U}^{an}_\pi \) . The Massey isomorphism is then defined by the composition:
\(\begin{tikzcd}\mathbb {D}\phi _f[r,"\simeq "] & \phi ^\pi _f\mathbb {D}[r,"(\tilde{T}_f^\pi )^{-1}"] & \phi _f\mathbb {D}\end{tikzcd}\) 
